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Rhombus Calculator

Calculate rhombus area, perimeter, side length, diagonals, altitude, and inradius with step-by-step geometric solutions.

Rhombus Metrics
Area
40
Side Length
6.4031
Perimeter
25.6125
Height (Altitude)
6.247
Deduction Steps:
Given diagonals d₁ = 10, d₂ = 8
Side: s = √((d₁/2)² + (d₂/2)²) = √(25 + 16) = 6.4031
Area: A = ½ × d₁ × d₂ = 0.5 × 10 × 8 = 40
Perimeter: P = 4s = 4 × 6.4031 = 25.6125
Height: h = A / s = 6.247
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What Is a Rhombus Calculator?

A rhombus is a quadrilateral whose four sides all have equal length. Opposite sides are parallel, and diagonals intersect perpendicularly (at 90°) while bisecting each other.

How to Use This Calculator

  1. Enter diagonal 1 (d₁) and diagonal 2 (d₂).
  2. View the calculated Area, Perimeter, Side Length, Height, and Inradius.
  3. Follow the step-by-step geometric deductions.

Rhombus Diagonals & Area Formulas

A = \frac{1}{2}d_1 d_2, \quad s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}, \quad P = 4s

Area is half the product of the two perpendicular diagonals. Side length is found via right triangles formed by the intersecting semi-diagonals.

Worked Example

Scenario: Find area and perimeter for diagonals d₁ = 12 and d₂ = 16

Area: A = ½ × 12 × 16 = 96

Semi-diagonals: 12/2 = 6, 16/2 = 8

Side length: s = √(6² + 8²) = √(36 + 64) = √100 = 10

Perimeter: P = 4 × 10 = 40

Result: Area = 96, Side = 10, Perimeter = 40

Tips & Key Notes

  • The diagonals of a rhombus always meet at right angles (90°).
  • If the angles of a rhombus are all 90°, it is a square.
  • Area can also be calculated as base times height: A = s × h.

Frequently Asked Questions

Why does area equal half the product of diagonals?

The diagonals divide the rhombus into four congruent right triangles. Summing their areas yields ½ × d₁ × d₂.

Are opposite angles equal in a rhombus?

Yes, opposite angles of a rhombus are equal, and adjacent angles are supplementary (they sum to 180°).

Can you calculate rhombus area with side and angle?

Yes, Area = s² × sin(θ), where θ is any interior angle.

What is the inradius of a rhombus?

The inradius is r = (d₁ × d₂) / (4s) = h / 2, representing the radius of the inscribed circle.

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